Single Photon Sources

Graham Jensen and Samantha To

University of Rochester, Rochester, New York

Abstract – Graham Jensen: We present the results of an investigation to verify the feasibility of

quantum dots and color-centered nanodiamonds as single photon sources. Using a confocal

microscope incorporated into a Hanbury Brown and Twiss setup, the antibunched nature of the

fluorescence of these sources is revealed. Along with a qualitative observation of antibunching in

a histogram, the fluorescence lifetime of quantum dots is measured. The average fluorescence

lifetime of quantum dots is determined to be ( ) . In addition to these parameters,

observations of the spectrum and atomic force microscope profiles of color-centered

nanodiamonds are recorded.

1. Introduction – Samantha To

Nanotechnology is a relatively young field that manipulates matter on atomic or

microscopic scale with the uses of quantum mechanics. It can be applied to a wide range of fields

such as organic chemistry, molecular biology and semiconductor physics because of the

numerous materials that exist at this microscopic scale. Specifically, quantum dots and

nanodiamonds have been researched and analyzed through optical procedures that have furthered

nanotechnology.

A semiconducting particle such as silicon, cadmium selenide and indium arsenide,

quantum dots has been at the scientific frontier of nanotechnology since the 1960’s. As a

semiconductor, it has a characteristic bandgap that allows the quantum dots to emit single

photons after laser excitation. Research in quantum dots has applications in optical storage,

LED’s, quantum computing and communication [1].

Found in crude oil, meteorites and interstellar dust, nanodiamonds or diamond

nanoparticles are a unique form of diamonds. Below a size of 3-6nm, it has been discovered that

diamond clusters become more stable than their graphite counterparts [2]. On the other hand,

nitrogen-vacancy-center nanodiamonds are not as stable as its pure form. In a photonic bandgap

cholesteric liquid crystal structure, nitrogen-vacancy-center nanodiamonds will emit single

photons after excitation [3].

Both quantum dots and nitrogen-vacancy-center nanodiamonds in photonic bandgap

cholesteric liquid crystal structure may be analyzed for specific characteristics. With the

Hanbury Brown and Twiss setup, antibunching of the emitted single photons and fluorescence

lifetime of both nanomaterials can be determined with a confocal fluorescence microscope. The

surface of the quantum dots and nanodiamonds can be analyzed with the use of an atomic force

microscope. Both a video of the blinking of quantum dots and the fluorescence spectroscopy of

nanodiamonds can be obtained with the conventional wide-view microscope.

2. Theory – Graham Jensen

The field of quantum cryptography promises the creation of indecipherably secure

communication utilizing the principles of quantum mechanics. Even with the advent of

extremely powerful quantum computers, the security of information transferred by quantum

communication systems remains unthreatened. While these systems offer great promise, their

implementation requires the use of non-classical light sources such as single photon sources: an

exacting requirement. Single photons sources were not realized until the late 1970s when an

experimental setup originally designed to show light’s bunched nature was used [4].

In 1956, Hanbury Brown and Twiss performed an experiment that revealed the

“bunching” tendency of photons: the phenomenon in which photons travel in close proximity to

each other rather than separately. Using a thermal source, Hanbury Brown and Twiss utilized a

half silvered mirror (beam splitter) and a correlation circuit setup to measure the coincidence of

photons and verify their bunched nature. An original sketch of their setup is seen in Fig. 1 [5].

For applications of quantum cryptography, individual photons must be separated in time and

space, a phenomenon known as antibunching. It was not until 20 years later that Hanbury Brown

and Twiss’s experimental setup was used to observe the first experimentally verified incidence

of antibunching.

Fig. 1. Original schematic of Hanbury Brown and Twiss’s experimental setup for the measurement of light’s

“bunched” nature

A University of Rochester group measured the first experimental observation of

antibunching. Using a Hanbury Brown and Twiss setup, Kimble et al. excited sodium atoms

with a laser to cause fluorescence [6]. In the fluorescence process, light is absorbed by a single

photon source promoting an electron to a higher energy state. While the electron is at this higher

energy level, other photons cannot be absorbed. After a period on the order of nanoseconds

(known as the fluorescence lifetime), the excited electron drops back to its ground state and

emits a single photon with energy corresponding to the energy difference between the excited

and ground states of the electron. A sketch of the energy transfer is seen in Fig. 2 [7]. If a laser

is continuously exciting a single sodium atom, a stream of emitted photons separated in time will

be observed due to the delay caused by the atom’s fluorescence lifetime. This was the

observation made by Kimble et al. and verified the phenomenon of antibunching [6].

Fig. 2. A diagram of the fluorescence process

The fluorescence lifetime of a single photon source can be described quantitatively by the

following equation:

where is the count number, is the maximum count value, and is the fluorescence lifetime.

If multiple single photon emitters are exited simultaneously, another exponential term is added to

the equation. Fluorescence lifetime is an essential characteristic of single photon sources.

In modern experimentation (like that performed in this course), an antibunching

histogram is measured to provide a quick test of the presence of antibunching. The histogram

shown in Fig. 3 shows the number of counts versus the time between the detection of photons at

“start” and “stop” detectors. The dip at the point indicates that the photons are separated

in time, i.e., antibunched [4].

Fig. 3. Histogram of time difference between incident photons

Quantitatively, antibunching is observed when the second order correlation function

value is less than one. The second order correlation function is written as

( ) ⟨ ( ) ( )⟩

⟨ ( )⟩⟨ ( )⟩

where is intensity, and are the time intervals, and ⟨ ⟩ is a time average. The value of

( ) varies for different types of light. For antibunched light, coherent light (like light from a

laser) and classical light, ( ) , ( ) , and ( ) respectively. In practical

applications, ( ) is defined as

( ) ( )

where ( ) is the number of coincidence counts, and are the intensities from each arm of a

Hanbury Brown and Twiss setup, is the time resolution, and is the total time [4].

For experiments in this course, quantum dots and nanodiamonds are used as single

photon sources. Quantum dots are semiconductors crystals with dimensions small enough to

exhibit quantum mechanical properties [6]. For use as a single photon source, the fluorescence

lifetime characteristics of quantum dots are utilized. Since quantum dots behave as a single

atom, it may only absorb and emit one photon at a time. This makes quantum dots an ideal

single photon source.

Nanodiamonds with color centers are diamond structures on the order of nanometers in

dimension. The title “color center” refers to an impurity in its internal structure that causes the

fluorescence of a certain wavelength of light [8]. For our experiments, a nitrogen vacancy

impurity is implemented but other impurities such as silicon, carbon, nickel, and chromium may

also be used [9]. For use as a single photon source, nanodiamonds are immersed in a photonic

bandgap host to enhance emission and ensure a definite polarization. In our case, a cholesteric

liquid crystal provided a one-dimensional bandgap that’s chiral nature allowed for the

transmission of left-handed circularly polarized light [6].

3. Experiment – Samantha To

This experiment was divided into different analysis processes that include determining

antibunching of single photons with the Hanbury Brown and Twiss setup, visualizing the surface

of the sample with the atomic force microscope, calculated the fluorescence lifetime with the

confocal fluorescence microscope and obtaining the fluorescence spectroscopy of the sample

with a conventional wide-view microscope. Quantum dots were used in obtaining antibunching,

a visual image of the surface and fluorescence lifetime. The nitrogen-vacancy-center

nanodiamond was used with the atomic force microscope, fluorescence lifetime reading and the

fluorescence spectroscopy.

3.1 Antibunching of single photons

To show antibunching of single photons, we used a red laser with 633nm excitation

wavelength and 0.49mW power to excite the quantum dot sample and the Hanbury Brown and

Twiss setup to detect the antibunched photons. A model of this setup is shown in Fig. 4 [4].

Fig. 4. Setup to determine antibunching of single photons due to fluorescence lifetime. The laser highlighted in

green hits the dichroic mirror that directs the photons to the objective where the sample is excited. The excited

sample emits single photons due to its fluorescent lifetime that enter the Hanbury Brown and Twiss setup with the

beam splitter and avalanche photodiodes.

When placing the sample on the objective, we need to add a small drop of oil immersion

to maximize the number of photons that enter the objective due to the difference in refractive

index. Fig. 5 shows visually how less photon emitted from the sample reach the objective when

air is between the objective and the glass slide than when oil is used [4].

Fig. 5. This diagram shows that less photons will enter the objective without the oil immersion due to the difference

in the index of refraction between the air and the glass slide.

For the safety of the avalanche photodiodes (APD), all light should be turned off. After

plugging in and turning on the APD’s and the excitation laser, we are ready to produce

antibunched photons. LabVIEW is used to provide a visual of the quantum dots as seen by both

detectors and TimeHarp is software that creates a histogram of the time difference between

photons obtained from both detectors. After specifying a region of the sample in micrometers

through LabVIEW, the program scans that area and produces an image showing the quantum

dots in that region. After manually picking a certain quantum dot, we can tell LabVIEW to go to

that quantum dot and TimeHarp to start recording to determine antibunching of the photons

emitted from this quantum dot. The electrical signals that are sent from the detectors are in the

form of Transistor-Transistor Logic (TTL) that are pulses of +5Volts and 30ns pulse duration.

3.2 Atomic force microscope

The atomic force microscope measures the surface of the sample through a series of

tapping with the cantilever as depicted in Fig. 6 [10]. The cantilever type used in this experiment

was the Tap190AI-G with a scan size of 25μm x 25μm. A 650nm laser was used in this setup

and a feedback loop from the NanoSurf EasyScan 2 program adjusted the z component of the

cantilever.

Fig. 6. Basic setup of the atomic force microscope. A laser beam is directed by the cantilever and the electronic

signal sent from the detector is interpreted by the computer program into an image of the sample at a nano-scale.

To begin analyzing the same, two things must occur. One, the program needs to be

calibrated with the auto frequency and two, the sample must be close enough for the cantilever to

begin oscillating. Once these two requirements have been filled, the cantilever is ready to begin

analyzing the surface of the sample, initiated with the “scan” button on the computer screen.

3.3 Fluorescence lifetime

Fluorescence lifetime is obtained with a similar setup as the determination of

antibunching of single photons. A green short-pulsed laser beam with 6ps pulses and 76

megaHertz frequency excites a sample which then emits single photons that are detected in the

Hanbury Brown and Twiss setup. The electrical outputs of the detectors are in the TTL format.

The difference between the antibunching setup and the fluorescence lifetime setup lies in the

following electronics. To determine the fluorescence lifetime, we need to measure the time

difference between photons with a designated start and stop signal. First, to calibrate the system,

the “zero time” is determined when the stop signal is the delayed negative pulses of the laser

beam and the start signal is fed from one of the APD’s. After calibrating, the electrical system

must be adjusted to obtain the time differences between consecutive photons. The start signal

remains the same while the stop signal is taken from the other APD and delayed with Ortec

425A to compensate for the computer resolution of 36ps. Because of the difference in electric

signals between the APD’s and the computer, an adaptor and attenuator is used to translate the

TTL signals in a BNC cable into low amplitude signals of 0.6volts in a 4-pin configuration. An

oscilloscope was used to confirm the electrical wiring of the system. The computer reads the start

and stop signal with a capacitor that begins charging with the start signal and stops with the stop

signal. Thus, the time difference is proportional to the voltage.

First procedural process is to obtain the “zero time”. Without scanning the sample, we ran

TimeHarp and obtained a single line the signaled the “zero time”. Just like the antibunching

procedure, we use LabVIEW to scan a region of the sample and determine a single nanoparticle.

Once the sample has been moved to view only the nanoparticle, TimeHarp is used to plot the

fluorescence lifetime of the nanoparticle.

3.4 Fluorescence spectroscopy

The fluorescence spectroscopy uses an EM-CCD camera and a diffracting grating as seen

in Fig. 7. A mirror redirects the photons emitted from the source, through a focus and diffracting

grating and into the detector connected to a computer. To obtain the fluorescence spectrum of

nanodiamonds, a green laser with 532nm excitation wavelength and 100.7μW power was used to

excite the nitrogen-vacancy-center nanodiamond in photonic bandgap cholesteric liquid crystal

structure.

Fig. 7. This is a diagram setup for the fluorescence spectroscopy with the use of an EM-CCD camera to view the

emissions of nanodiamonds excited by the green laser. Mirrors were used to redirect the photon beam through a

focus.

The software called Andor SOLIS for Imaging was used to obtain the spectroscopy plots

of both the green laser beam and the nanodiamonds. This software would first display an image

of the intensity of the photons relative to its wavelength and then translate these intensities into a

histogram showing the relative wavelengths emitted from each source.

4. Results – Graham Jensen

4.1 Quantum Dots

A raster scan performed by a confocal microscope setup utilizing LabVIEW

software revealed single emitter quantum dots in a pre-prepared sample. An image output from a

LabVIEW program of this scan is seen in Fig. 8.

Fig. 8. A raster scan image of a large number of quantum dots excited by a 49mW 633nm HeNe laser

with 2 orders of magnitude attenuation filters.

With the positions of the quantum dots revealed, a focused beam can be directed on an

individual quantum dot. By exciting just one quantum dot, the emitted florescence will be

characterized as antibunched light. A Hanbury Brown and Twiss setup along with a TimeHarp

computer card records the time between photons incident on a pair of avalanche photodiodes.

This data is represented well as a histogram of counts versus time delay between photons. A

sample of two measurements of antibunching is seen in Fig. 9 and Fig. 10.

Fig. 9. A curser is placed on the desired quantum dot for scanning in a LabVIEW program (left), the resulting

histogram of counts versus time delay (right). Note the dip in the histogram indicative of antibunching.

Fig. 10. Another measurement of antibunching.

As mentioned earlier, the fluorescence phenomenon is the essential feature of quantum

dots that make them ideal for use as a single photon source. The fluorescence lifetime is the time

it takes on average for the count rate to drop to the maximum count rate divided by e. A typical

fluorescence lifetime histogram is seen in Fig. 11.

Fig. 11. A histogram of the time delay between signals of a single quantum dot.

A histogram and table of values for ten fluorescence lifetime measurements was taken to

determine the average value of for a sample of quantum dots. For most cases, the fluorescence

lifetime equation could be manipulated to into a linear equation for easy analysis as seen below.

( )

( )

In this format, the slope of the line is the negative inverse of the fluorescence lifetime. However,

not all of the collected data followed this simple trend. Occasionally, more than one quantum

dot was excited and the fluorescence of multiple quantum dots was recorded. For this case, the

following equation was used to fit the measured data using Microsoft Excel’s solver function.

A table of the derived fluorescence lifetimes is seen below (Fig. 12).

Fig. 12. Table of measured fluorescence lifetimes

As stated in the table, the average measured fluorescence lifetime of the sampled

quantum dots is ( ) .

Another interesting property of quantum dots is their spontaneous blinking or alternating

periods of active and less active fluorescence. This property is observable with wide field

microscopy and in plots of intensity versus time. Images of both of these events are seen below

in Fig. 13. and Fig. 14.

Fig. 13. A wide field microscopy image of fluorescing quantum dots taken with an EM-CCD camera

Fig. 14. A confocal microscope is focused on a quantum dot (left) and the resulting intensity versus time plot (right)

are seen. Note the time gaps between intensity maxima or “blinking”.

4.2 Nanodiamonds

Along with quantum dots, color centered nanodiamonds immersed in a cholesteric liquid

crystal solution also work well as a single photon source. The size and shape nanodiamonds are

directly observable using an atomic force microscope (AFM). The AFM used for our

experiments is calibrated by examining a silicon calibration sample. A few of the patterns are

seen below in Fig. 15.

Fig. 15. A subset of calibration examples from a silicon AFM calibration sample. Height calibration, “Lego”

pattern, and “Inverse Lego” pattern (From left to right)

With proper calibration ensured, the AFM can be used to examine nanodiamonds in a

CLC solution. Fig. 16 shows a scan of many nanodiamonds as well as a smaller scan

centered on a single nanodiamond.

Fig. 16. A scan of a nanodiamond sample with a zoom box centered on a single nanodiamond (left) and

the zoomed region (right).

A CLC solution and nanodiamond mixture was analyzed using a confocal microscope

and Hanbury Brown and Twiss setup. Below is an image taken with an EM-CCD camera of the

sample studied with wide field microscopy (Fig. l7).

Fig. l7. Wide field microscopy image of color-centered nanodiamond sample taken with EM-CCD camera

The sample was analyzed with a confocal microscope and Hanbury Brown and Twiss

setup using a raster scan. An image of the sample’s fluorescence as well as a

histogram depicting the fluorescence lifetime are seen in Fig. 18 and Fig. 19.

Fig. 18. raster scan of color-centered nanodiamonds in CLC solution

Fig. 19. Histogram of counts versus time delay between photons. Data can be analyzed to determine the

fluorescence lifetime

The spectrum of the fluorescence of color-centered nanodiamonds in CLC solution can

be analyzed using a spectrometer consisting of a diffraction grating and EM-CCD camera. A

pre-made calibration file converts pixel numbers on the EM-CCD camera into wavelength as

separated by a diffraction grating. Fig. 20 shows the raw data taken by the EM-CCD camera as

well as the spectrum determined by processing this data.

Fig. 20. Raw data from the EM-CCD camera (left) and corresponding spectrum of a 10 second exposure (right).

Note the large spike at 523nm caused by light from the green pump laser leaking into our setup. The bump in the

nanodiamonds’ spectrum is centered at ~690nm. The registration of the green laser at 523nm indicates the

calibration is ~8 nm off (green light is 532nm).

5. Conclusion – Samantha To

Characteristics of nanoparticles such as quantum dots and nanodiamonds were

investigated in this paper. LabVIEW was used to image the samples and focus on single

nanoparticles. While many sets of data show no antibunching because we had focused on a group

of single nanoparticles, which collectively would not exhibit antibunching, antibunching did

occur for when we were able to narrow down on single nanoparticles. The fluorescence lifetime

of both quantum dots and nanodiamonds was calculated to be ( ) . An image of

the surface of each sample of nanoparticles was obtained with the atomic force microscope as

well as the fluorescence spectroscopy of the nanodiamonds with the EM-CCD camera.

6. References

[1] Gammon, D; Steel, D. “Optical Studies of Single Quantum Dots”, Phys. Today. 55, No. 10

(2002).

[2] Badziag, P.; Verwoerd, W.S.; Ellis, W.P.; Greiner, N.R. Nanometre-sized diamonds are

more stable than graphite. Nature 1990, 343, 244-245.

[3] Aharonovich, I.; Greentree, A. D.; Prawer, S. (2011). "Diamond photonics". Nature

Photonics 5 (7): 397–405.

[4] Lukishova, S. G., “Single photon sources for secure quantum communication”,

http://www.optics.rochester.edu/workgroups/lukishova/QuantumOpticsLab/

[5] Brown, R. Hanubury, Twiss, R. Q., “Correlation Between Photons in Two Coherent Beams

of Light”, Nature 177, 27-32 (1956).

[6] Kimble, H. J., Dagenais, M., Mandel, L., “Photon Antibunching in Resonance

Fluorescence”, Phys. Rev. Lett. 39, 691-695 (1977).

[7] Lukishova, S. G., “Labs 3-4. Single Photon Source”,

http://www.optics.rochester.edu/workgroups/lukishova/QuantumOpticsLab/.

[8] Mochalin, Vadym N., Shenderova, Olga, Ho, Dean, Gogotsi, Yury, “The properties and

applications of nanodiamonds”, Nature Nanotechnology 7, 11-23 (2012).

[9] Hausmann, Birgit J. M., Babinec, Thomas M., Choy, Jennifer T., Hodges, Jonathan S.,

Hong, Sungkun, Bulu, Irfan, Yacoby, Amir, Lukin, Mikhail D., Loncar, Marko, “Single-color

centers implanted in diamond nanostructures”, New J. Phys. 13, 1-10 (2011).

[10] Ron Reifenberger; Arvind Raman, "ME 597/PHYS 570: Fundamentals of Atomic Force

Microscopy (Fall 2009),"https://nanohub.org/resources/7320.